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A159299
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Number of n-colorings of the 4 X 4 Sudoku graph.
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2
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0, 0, 0, 0, 288, 166560, 33539040, 2350746720, 75756999360, 1388552614848, 16744788486720, 146769785743680, 1002373493948640, 5606534724167520, 26640793339768608, 110556058012152480, 409297168707073920, 1374572399886053760, 4243833928227876480
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| The 4 X 4 Sudoku graph is a septic graph on 16 vertices and 56 edges. a(n) gives the number of 4 X 4 Sudoku solutions, if each of up to n numbers is allowed only once in every row, column and block.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..1000
Timme, Marc; van Bussel, Frank; Fliegner, Denny; Stolzenberg, Sebastian (2009) "Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions", New J. Phys. 11 023001, doi: 10.1088/1367-2630/11/2/023001.
Eric Weisstein's World of Mathematics, Chromatic Polynomial
Wikipedia, Mathematics of Sudoku
Wikipedia, Sudoku
Wikipedia, Sudoku algorithms
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FORMULA
| a(n) = n^16 -56*n^15 + ... (see Maple program).
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EXAMPLE
| For n=4 colors one of the 288 possible colorings is given by this Sudoku:
+---+---+
|1 2|3 4|
|4 3|2 1|
+---+---+
|3 1|4 2|
|2 4|1 3|
+---+---+
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MAPLE
| a:= n-> n^16 -56*n^15 +1492*n^14 -25072*n^13 +296918*n^12 -2621552*n^11 +17795572*n^10 -94352168*n^9 +392779169*n^8 -1279118840*n^7 +3217758336*n^6 -6107865464*n^5 +8413745644*n^4 -7877463064*n^3 +4436831332*n^2 -1117762248*n: seq (a(n), n=0..20);
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CROSSREFS
| Cf. A107739, A182866.
Sequence in context: A163007 A069329 A037946 * A008695 A047805 A173150
Adjacent sequences: A159296 A159297 A159298 * A159300 A159301 A159302
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Apr 09 2009
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